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arXiv · 0706.3218

Computing word length in alternate presentations of Thompson's group F

Matthew Horak·Melanie Stein·Jennifer Taback
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Abstract

We introduce a new method for computing the word length of an element of Thompson's group F with respect to a "consecutive" generating set of the form X_n={x_0,x_1,...,x_n}, which is a subset of the standard infinite generating set for F. We use this method to show that (F,X_n) is not almost convex, and has pockets of increasing, though bounded, depth dependent on n.

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Matthew Horak, Melanie Stein, Jennifer Taback. 2007-06-22. Computing word length in alternate presentations of Thompson's group F. https://doi.org/10.1142/s0218196709005445

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